p_laplacian_circle.h

The p-Laplacian problem on a circular geometry – exact solution

struct u_exact {
Float operator() (const point& x) const {
return (1 - pow(norm2(x), p/(2*p-2)))/((p/(p-1))*pow(2.,1/(p-1)));
}
u_exact (Float q) : p(q) {}
protected: Float p;
};
struct grad_u {
point operator() (const point& x) const {
return - (pow(norm2(x), p/(2*p-2) - 1)/pow(2.,1/(p-1)))*x;
}
grad_u (Float q) : p(q) {}
protected: Float p;
};
Float
see the Float page for the full documentation
point
see the point page for the full documentation
rheolef::norm2
T norm2(const vec< T, M > &x)
norm2(x): see the expression page for the full documentation
Definition: vec.h:379
rheolef::pow
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition: space_mult.h:120
grad_u
Definition: combustion_exact.icc:34
grad_u::operator()
point operator()(const point &x) const
Definition: combustion_exact.icc:35
grad_u::p
Float p
Definition: p_laplacian_circle.h:37
grad_u::grad_u
grad_u(Float lambda, bool is_upper)
Definition: combustion_exact.icc:37
p
Definition: sphere.icc:25
u_exact
Definition: interpolate_RTk_polynom.icc:125
u_exact::operator()
point operator()(const point &x) const
Definition: interpolate_RTk_polynom.icc:126
u_exact::u_exact
u_exact(size_t d1, Float w1=acos(Float(-1)))
Definition: interpolate_RTk_polynom.icc:144
u_exact::p
Float p
Definition: p_laplacian_circle.h:30